Given a path integral for a system
$$Z(\phi) = \int [D\phi] e^{-S[\phi]},$$
where I am working in the Euclidean signature, necessarily mean that the system described is quantum mechanical? In the equation above, I am looking at $(d+1)$ dimensional field theories, such that $d=0$ Feynman path integral is standard quantum mechanics, and $d>0$ Feynman path integral means QFTs. Periodicity in the Euclidean time similarly gives the thermal partition function of the quantum system.
To pose this question more precisely, are there path integrals of the above form corresponding to which there exist no canonical formulation of quantum mechanics. A provocative example might be the Martin-Siggia-Rose stochastic path integral, which seemingly admits no quantum description. However it is dual to a microscopic description of a Brownian particle interacting with a bath if viewed in the Schwinger Keldysh formalism. Thus it defines a quantum system. My question is do all path integrals admit a description in the canonical quantum mechanical formulation, be it a direct or an indirect dual interpretation; or are there obstructions to such interpretations for certain classes of path integrals?